Benford’s law for accounting data

In a previous post I noted how the sizes of data breaches seem follow Benford’s law. It’s not too hard to imagine that hackers penetrating one or more layers of security can lead to a multiplication in their success for each layer he penetrates. And because data that’s created by exponential growth or some sort of multiplicative process tends to follow Benford’s law, we shouldn’t be too surprised when we see that the size of data breaches follow it.

Accountants sometimes use Benford’s law to find fraudulent accounting data. This is based on the observation that lots of real accounting data follows this law while numbers that are fraudulently created often don’t, so that if you’re an auditor and you find accounting data that violates Benford’s law too badly that might an indication that you’ve discovered some sort of fraud.

But why would you expect accounting data to follow Benford’s law?

I recently asked several accountants who’ve worked in internal audit groups why they think that accounting data should follow this law and none of them could think of any good reason. So when I recently had some time to kill while waiting for a flight from Houston to San Jose, I thought about this for a few minutes and I came to the conclusion that this probably happens because of inflation. Inflation is an example of exponential growth, and that’s the very sort of process that tends to lead to data that follows Benford’s law.

That seems to be as good as any other explanation that I’ve heard of, but then those have all been along the lines of “well, we really don’t know.”

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